Question

Find the equation of the exponential function represented by the table below:

х
Y
0
3
1
1.5
2
0.75
3
0.375

Answer 1

Given:

The table of values.

To find:

The equation of the exponential function represented by the table.

Solution:

The general form of an exponential function is

`y=ab^x` ...(i)

where, a is initial value and b is growth factor.

From the given table it is clear that the function passes through (0,3) and (1,1.5). So, the must be satisfy by these points.

Putting x=0 and y=3 in (i), we get

`3=ab^0`

`3=a(1)`

`3=a`

Putting a=3, x=1 and y=1.5 in (i), we get

`1.5=3b^1`

`(1.5)/(3)=b`

`(1)/(2)=b`

Putting
`a=3` and
`b=(1)/(2)` in (i), we get

`y=3\left((1)/(2)\right)^x`

Therefore, the required equation for exponential function is
`y=3\left((1)/(2)\right)^x`.